The Florida pastor who sparked an international crisis with his plan to burn hundreds of Qur'ans has given an undertaking that he will not carry out the stunt, after an intervention by Barack Obama warning he would put American lives at risk.

The promise from Terry Jones, head of a congregation of about 50 at the Dove World Outreach Centre in Gainesville, came after 48 hours in which he made frequent changes of mind. Having announced on Thursday that he would cancel the stunt, Jones appeared to backtrack yesterday.

In the latest of a bizarre series of twists, he and an evangelical colleague, KA Paul, from Texas, appeared on television and issued a two-hour deadline to Feisal Abdul Rauf, the imam at the centre of the row in New York over the siting of a mosque and Islamic cultural centre near Ground Zero.

They demanded he meet them in New York and agree to move the proposed buildings to another location. The deadline passed without any response from Rauf.

Paul and Jones then told reporters that they still intended to make the trip to New York. Paul added that Jones would not carry out the Qur'an burning.

Earlier, Obama attempted to defuse the crisis, which yesterday claimed several lives as thousands of Afghans protested against the possible desecration of the Qur'an. Speaking at a White House press conference, Obama called on Jones to abandon his plan. "My hope is that this individual prays on it and refrains from it," the president said.

In Afghanistan, two people were killed and several injured when police shot protesters in the north-eastern city of Faizabad. Reports from Farah province in western Afghanistan said one civilian was killed and three wounded in violence which erupted when several thousand protesters gathered outside a Nato base in the Bala Baluk district of Farah province.

The face-off between Obama and the Florida pastor came as feelings were running high across the country, with a series of ceremonies planned to mark 9/11 and rallies in New York for and against the proposed Islamic centre.

Obama issued a blunt warning to Jones and any copycats who might tempted to issue similar threats to burn Qur'ans to gain publicity. In a rare show of emotion, he said burning Qur'ans would risk the lives of young Americans serving in the military in Afghanistan, Iraq and elsewhere round the world. "This is a way of endangering our troops, our sons and daughters … you don't play games with that," he said.

Jones was adamant on Wednesday that he was going to burn the Qur'an but by Thursday morning, in the face of increasing pressure, he was having second thoughts. After a phone call from the defence secretary, Robert Gates, Jones said he was cancelling the stunt and claimed he was doing so after securing talks with Rauf and a promise that the New York mosque and cultural centre was being moved.

But Rauf issued a statement saying: "I am prepared to consider meeting with anyone who is seriously committed to pursuing peace. We have no such meeting planned at this time. Our plans for the community centre have not changed."

A Florida imam, Muhammad Musri, had been in discussion with Jones, who portrayed him as a go-between with Muslims in New York. When Rauf denied any plan to move to a new location or to have organised any meeting, Jones accused Musri of having "clearly lied to us". Musri, from the Islamic Society of Central Florida, said Jones had "stretched and exaggerated" their conversation.

Obama's press conference, which the White House had hoped would focus on plans to revive the economy, was instead dominated by questions about Islam, including whether relations with Muslims in America and elsewhere round the world had deteriorated over the last nine years.

Obama told reporters: "The idea that we would burn the sacred text of someone else's religion is contrary to what this country stands for."

The president suggested that blame for the extensive coverage that Jones's threat had received lay with the media, not the White House. "I hardly think we were the ones who elevated this story. But it is something, in the age of the internet, something that can cause us profound damage around the world, so we have to take it seriously," Obama said.